Asymptotic shallow water models for internal waves in a two-fluid system with a free surface

In this paper, we derive asymptotic models for the propagation of two and three-dimensional gravity waves at the free surface and the interface between two layers of immiscible fluids of different densities, over an uneven bottom. We assume the thickness of the upper and lower fluids to be of comparable size, and small compared to the characteristic wavelength of the system (shallow water regimes). Following a method introduced by Bona, Lannes and Saut based on the expansion of the involved Dirichlet-to-Neumann operators, we are able to give a rigorous justification of classical models for weakly and strongly nonlinear waves, as well as interesting new ones. In particular, we derive linearly well-posed systems in the so called Boussinesq/Boussinesq regime. Furthermore, we establish the consistency of the full Euler system with these models, and deduce the convergence of the solutions.Comment: 32 pages, 4 figure

Decay and return of internal solitary waves with rotation

Author Posting. © The Author, 2007. This is the author's version of the work. It is posted here by permission of American Institute of Physics for personal use, not for redistribution. The definitive version was published in Physics of Fluids 19 (2007): 026601, doi:10.1063/1.2472509.The effect of rotation on the propagation of internal solitary waves is examined. Wave evolution is followed using a new rotating extension of a fully-nonlinear, weakly nonhydrostatic theory for waves in a two-layer system. When a solitary wave solution of the non-rotating equations is used as the initial condition the wave initially decays by radiation of longer inertia-gravity waves. The radiated inertia-gravity wave always steepens, leading to the formation a secondary solitary-like wave. This decay and re-emergence process then repeats. Eventually a nearly localized wavepacket emerges. It consists of a longwave envelope and shorter, faster solitary-like waves that propagate through the envelope. The radiation from this mature state is very weak, leading to a robust, long-lived structure that may contain as much as 50% of the energy in the initial solitary wave. Interacting packets may either pass through one another, or merge to form a longer packet. The packets appear to be modulated, fully-nonlinear versions of the steadily translating quasi-cnoidal waves.This work was supported by a Woods Hole Oceanographic Institution Mellon Independent Study Award and ONR Grant N000140610798

Chandra X-ray Observation of a Mature Cloud-Shock Interaction in the Bright Eastern Knot Region of Puppis A

We present Chandra X-ray images and spectra of the most prominent cloud-shock interaction region in the Puppis A supernova remnant. The Bright Eastern Knot (BEK) has two main morphological components: (1) a bright compact knot that lies directly behind the apex of an indentation in the eastern X-ray boundary and (2) lying 1' westward behind the shock, a curved vertical structure (bar) that is separated from a smaller bright cloud (cap) by faint diffuse emission. Based on hardness images and spectra, we identify the bar and cap as a single shocked interstellar cloud. Its morphology strongly resembles the ``voided sphere'' structures seen at late times in Klein et al.'s experimental simulations of cloud-shock interactions, when the crushing of the cloud by shear instabilities is well underway. We infer an interaction time of roughly 3 cloud-crushing timescales, which translates to 2000-4000 years, based on the X-ray temperature, physical size, and estimated expansion of the shocked cloud. This is the first X-ray identified example of a cloud-shock interaction in this advanced phase. Closer to the shock front, the X-ray emission of the compact knot in the eastern part of the BEK region implies a recent interaction with relatively denser gas, some of which lies in front of the remnant. The complex spatial relationship of the X-ray emission of the compact knot to optical [O III] emission suggests that there are multiple cloud interactions occurring along the line of sight.Comment: 22 pages LaTeX with multiple figures, to appear in Ap

Ionization States and Plasma Structures of Mixed-morphology SNRs Observed with ASCA

We present the results of a systematic study using ASCA of the ionization state for six ``mixed-morphology'' supernova emnants (MMSNRs): IC 443, W49B, W28, W44, 3C391, and Kes 27. MMSNRs show centrally filled thermal X-ray emission, which contrasts to shell-like radio morphology, a set of haracteristics at odds with the standard model of SNR evolution (e.g., the Sedov model). We have therefore studied the evolution of the MMSNRs from the ionization conditions inferred from the X-ray spectra, independent of X-ray morphology. We find highly ionized plasmas approaching ionization equilibrium in all the mmsnrs. The degree of ionization is systematically higher than the plasma usually seen in shell-like SNRs. Radial temperature gradients are also observed in five remnants, with cooler plasma toward the limb. In IC 443 and W49B, we find a plasma structure consistent with shell-like SNRs, suggesting that at least some MMSNRs have experienced similar evolution to shell-like SNRs. In addition to the results above, we have discovered an ``overionized'' ionization state in W49B, in addition to that previously found in IC 443. Thermal conduction can cause the hot interior plasma to become overionized by reducing the temperature and density gradients, leading to an interior density increase and temperature decrease. Therefore, we suggest that the ``center-filled'' X-ray morphology develops as the result of thermal conduction, and should arise in all SNRs. This is consistent with the results that MMSNRs are near collisional ionization equilibrium since the conduction timescale is roughly similar to the ionization timescale. Hence, we conclude that MMSNRs are those that have evolved over$\sim10^4$ yr. We call this phase as the ``conduction phase.''Comment: 34 pages, 20 figures, 9 tables, accepted for publication in The Astrophysical Journa

The Radial Structure of the Cygnus Loop Supernova Remnant --- Possible evidence of a cavity explosion ---

We observed the North-East (NE) Limb toward the center region of the Cygnus Loop with the ASCA Observatory. We found a radial variation of electron temperature (kTe) and ionization timescale (log(\tau)) whereas no variation could be found for the abundances of heavy elements. In this paper, we re-analyzed the same data set and new observations with the latest calibration files. Then we constructed the precise spatial variations of kTe, log(\tau), and abundances of O, Ne, Mg, Si, and Fe over the field of view (FOV). We found a spatial variation not only in kTe and in log(\tau) but also in most of heavy elements. As described in Miyata et al. (1994), values of kTe increase and those of log(\tau) decrease toward the inner region. We found that the abundance of heavy elements increases toward the inner region. The radial profiles of O, Ne, and Fe show clear jump structures at a radius of 0.9 Rs, where Rs is the shock radius. Outside of 0.9 Rs, abundances of all elements are constant. On the contrary, inside of 0.9 Rs, abundances of these elements are 20--30 % larger than those obtained outside of 0.9 Rs. The radial profile of kTe also shows the jump structure at 0.9 Rs. This means that the hot and metal rich plasma fills the volume inside of 0.9 Rs. We concluded that this jump structure was the possible evidence for the pre-existing cavity produced by the precursor. If the ejecta fills inside of 0.9 Rs, the total mass of the ejecta was roughly 4\Msun. We then estimated the main-sequence mass to be roughly 15\Msun, which supports the massive star in origin of the Cygnus Loop supernova remnant and the existence of a pre-existing cavity.Comment: 37 pages, 14 figures. Accepted for publication of Ap

Discovery of the compact X-ray source inside the Cygnus Loop

We detected an X-ray compact source inside the Cygnus Loop during the observation project of the whole Cygnus Loop with the ASCA GIS. The source intensity is 0.11 c s$^{-1}$ for GIS and 0.15 c s$^{-1}$ for SIS, which is the strongest in the ASCA band. The X-ray spectra are well fitted by a power law spectrum of a photon index of \error{-2.1}{0.1} with neutral H column of (\error{3.1}{0.6})${\rm \times 10^{21} cm^{-2}}$. Taking into account the interstellar absorption feature, this source is X-ray bright mainly above 1 keV suggesting either an AGN or a rotating neutron star. So far, we did not detect intensity variation nor coherent pulsation mainly due to the limited observation time. There are several optical bright stellar objects within the error region of the X-ray image. We carried out the optical spectroscopy for the brightest source (V=+12.6) and found it to be a G star. The follow up deep observation both in optical and in X-ray wavelengths are strongly required.Comment: Accepted for Publications of the Astronomical Society of Japan 17 pages, 3 figur